SZ Mon, the double pulsator
Observed: 35 sessions from 23 Dec 2005 to 11 Mar 2007
| Lloyd Evans (1970)
|AFOEV (V mag)||1999||10.6||10.8|
SZ Mon is the bright object near the cross hair, it looks elongated. The image width is 6', North is up, East is left.
At the East of SZ Mon, a few arcseconds away, there is a fairly bright
star. The above magnitudes include the contribution from this star. Let
be m the measured magnitude (the sum of SZ Mon and of the nearby star).
The magnitude of SZ Mon, mSZ, can then be computed
mSZ = m + 2.5*log[1+k*10^(mSZ/2.5)]
with k a constant (assuming the nearby star is constant).
k is computed by analyzing the East-West profile when SZ Mon is near a minimum so as to have a better view of the nearby star:
I did this analysis with 3 images taken with the B filter and 3 images
with the V filter. The results are:
average kB = 1.022E-5 (standard deviation 0.115E-5)
average kV = 1.421E-5 (standard deviation 0.061E-5)
The magnitudes of SZ Mon with the nearby star substracted are HERE. (I did not propagate the standard deviation on k because, whatever the error on k is, k is constant in time).
I can also compute the magnitudes of the nearby star: B=12.480 V=12.119, and its distance to SZ Mon: 6". (B-V=0.36 so the star is not red and unlikely a variable).
The measured b,v magnitudes may be transformed
for the instrument response. The transformed B,V magnitudes are then:
V = v + TvTbv*[(b-v)-(Bc-Vc)]
B = b + TbTbv*[(b-v)-(Bc-Vc)]
Bc,Vc are the magnitudes of the comparison star. The transformation coefficients were measured HERE; they are:
TbTbv = 0.002+/-0.027
TvTbv = -0.025+/-0.015
The transformed magnitudes are HERE.
The B-V color as a function of the V magnitude is then:
Red dots: phase [0.8,0.3[ i.e. the pulse at phase 0.0;
Blue dots: phase [0.3,0.8[ i.e. the pulse at phase 0.5;
for these dots, the magnitudes are substracted for the nearby star and are transformed.
Magenta small crosses: the raw magnitudes.
The diagram is run twice per period, in the direction of the arrows.
The star is bluer when it becomes brighter. The two pulses run the same loop diagram.
Compared with the 1999 AFOEV observations, SZ Mon looks more bluish
in 2006, especially when the intensity is rising:
Magenta dots: my observations (2006); Blacks dots: AFOEV observations (1999).
There are 28 pairs of B,V measurements for 39 individual measurements
in V and 33 in B. To be able to interpolate, the V and B magnitudes are
fitted with the following functions of the phase:
Red dots: the V measurements with the nearby star subtracted;
Red line: the pVf(p) function;
Blue: the same for the B filter.
The resulting B-V versus phase diagram:
Blue line: the pBf(p)-pVf(p) function corrected for the transformation;
Red: the measured B-V color. The error bars are the 1-sigma statistical uncertainties, corrected for the nearby star and the uncertainties on the transformation coefficients.
According to Reed (1998) the effective temperature T (°K) can be computed
as a function of B-V:
B-V = -3.684*log(T) + 14.551 (when T below 9100°K)
Barnes and Evans (1976) considered a large number of measured star diameters (from occultation, interferometry, etc) and discovered the following empirical relation between the angular diameter phi (in milliarcseconds), the V magnitude and the B-V color:
4.2207 -0.1*V -0.5*log(phi) = 3.964 - 0.333*(B-V)
The effective temperature and the angular diameter can then be computed as a function of the phase:
It looks like the temperature and diameter are not exactly synchronized: when the radius is maximum, the temperature is near its minimum and will continue to decrease for a little while as the radius starts to diminish.
RV Tau stars have an absolute magnitude around M=-4 (there are at the
upper right part of the Hertzprung-Russel diagram). SZ Mon is observed
with an average magnitude m=10.47 (V filter, with the nearby star substracted,
transformed). The distance to SZ Mon is then:
d = 10^(m-M+5)/5 = 7.8kpc = 23,000lyr
The radius is then around 80 solar radii:
The absolute V magnitudes Mv (at 10pc) may be computed from the measured
V magnitudes and the distance d:
Mv = 5 + V - 5*log(d)
The luminosity L(p) as a function of phase p is then (in Sun luminosity unit):
L(p) = 10^(Mv(p)-Mov+BC(T)-BC(To))/-2.5
where Mov=4.89 is the Sun absolute V magnitude, To=5780°K its effective temperature, and BC is the bolometric correction. BC, a function of the effective temperature, is given by Reed (1998) as:
BC(T) = C6*(log(T)-4)^4 + C7*(log(T)-4)^3 + C8*(log(T)-4)^2 + C9*(log(T)-4) + C10
with C6=-8.499 C7=13.421 C8=-8.131 C9=-3.901 C10=-0.438.
The luminosity is then around 7,000 times the solar luminosity:
The interstellar absorption Av in V can be computed as a function
of the interstellar reddening E(B-V) as:
Av=R*E(B-V) with R=3.1 for the Milky Way.
The above calculations can then be redone as a function of E(B-V):
Green: the distance (in pc);
Blue: the average effective temperature (in °K);
Red: the average luminosity (in solar luminosities).
The average radius (in solar radii) as a function of the reddening.
Barnes T.G., Evans D.S. (1976) MNRAS 174 489.
Lloyd Evans T. (1970) The Observatory 90 254.
Mamajek E.E., Meyer M.R., Liebert J. (2002) AJ 124 1670 Appendix
erratum (2006) AJ 131 2360.
Pojmanski G. (2002) Acta Astronomica 52 397.
Reed C. (1998) J. RAS of Canada 92 36.
Stobie R.S. (1970) MNRAS 148 1.
This amateur research has made use of the AFOEV database, operated at CDS (France) and of SkyDot/ROTSE-I/NSVS data.
Pulsating stars and its links.
TX Mon (a Cepheid) in the same field of view.
Similar determinations of the temperature, radius and luminosity are HERE.
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